There's two ways to rotate an image. One is by actually moving the pixels around. This works in all situations but can reduce quality a little on JPEGs.
The other way is by putting a hint in the EXIF header that says, "hey, when you display this, flip it first." Camera software often does it this way.
I can't tell exactly what's going on with your image, but I'm guessing it's something related. It doesn't seem to have an EXIF header but it may be the site is stripping it out...

This is a very common problem, one that I've never fully figured out. It seems to happen more often with Iphone photos. It's been discussed a lot and a couple folks have proposed solutions, but they were pretty well incomprehensible to me. I just turn my lap top...............